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http://dx.doi.org/10.4134/CKMS.c190365

REMARKS ON THE LIECHTI-STRENNER'S EXAMPLES HAVING SMALL DILATATIONS  

Ham, Ji-Young (Department of Science Hongik University)
Lee, Joongul (Department of Mathematics Education Hongik University)
Publication Information
Communications of the Korean Mathematical Society / v.35, no.4, 2020 , pp. 1299-1307 More about this Journal
Abstract
We show that the Liechti-Strenner's example for the closed nonorientable surface in [13] minimizes the dilatation within the class of pseudo-Anosov homeomorphisms with an orientable invariant foliation and all but the first coefficient of the characteristic polynomial of the action induced on the first cohomology nonpositive. We also show that the Liechti-Strenner's example of orientation-reversing homeomorphism for the closed orientable surface in [13] minimizes the dilatation within the class of pseudo-Anosov homeomorphisms with an orientable invariant foliation and all but the first coefficient of the characteristic polynomial p(x) of the action induced on the first cohomology nonpositive or all but the first coefficient of p(x)(x ± 1)2, p(x)(x2 ± 1), or p(x)(x2 ± x + 1) nonpositive.
Keywords
Minimal dilatation; nonorientable surface; Liechti-Strenner; pseudo-Anosov stretch factors;
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